LiMM-PCA with Elk time series data
Sam Pannoni
February 28, 2022
1 Data set up
# manon_design<- design
# manon_outcomes <- outcomes
# import data ####
# elk_rdp_ASV_iQlr.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_ASV_iQlr.ps.rds")
# elk_rdp_genus_iQlr.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_genus_iQlr.ps.rds")
# elk_rdp_spp_iQlr.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_spp_iQlr.ps.rds")
#CoDa conforming CLR (dont subset further)
# elk_rdp_ASV_CLR.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_ASV_CLR.ps.rds")
# elk_rdp_day0_CLR.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_day0_CLR.ps.rds")
# elk_rdp_genus_CLR.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_genus_CLR.ps.rds")
elk_rdp_spp_CLR.ps <- readRDS(file = "r_output/intermediate_rds_files/elk_rdp_spp_CLR.ps.rds")
# elk_rdp_genus_CLR_no14.ps<- phyloseq::subset_samples(elk_rdp_genus_CLR.ps, Day != 14)
# df1.CLRday0 <- as.data.frame(elk_rdp_day0_CLR.ps@otu_table)
# df2.CLRasv <- as.data.frame(elk_rdp_ASV_CLR.ps@otu_table)
# df3.CLRgen <- as.data.frame(elk_rdp_genus_CLR.ps@otu_table)
# df3.CLRgen_no14 <- as.data.frame(elk_rdp_genus_CLR_no14.ps@otu_table)
df4.CLRspp <- as.data.frame(elk_rdp_spp_CLR.ps@otu_table)
# df1.iQlrASV <- as.data.frame(elk_rdp_ASV_iQlr.ps@otu_table)
# df2.iQlrGen <- as.data.frame(elk_rdp_genus_iQlr.ps@otu_table)
# df3.iQlrSpp <- as.data.frame(elk_rdp_spp_iQlr.ps@otu_table)
###
### ID names Volunteer Sampling Tube Time
# 10111 1 10111 10 1 1 1
# 10112 2 10112 10 1 1 2
design <- elk_rdp_spp_CLR.ps@sam_data
# design <- elk_rdp_genus_CLR_no14.ps@sam_data
design2 <- data.frame("Day" = as.factor(design$Day),
"Time" = as.numeric(design$Day),
"Elk" = as.factor(design$Elk),
"Rep" = as.factor(design$Rep),
"ID" = design$Description,
row.names = design$Description)
design2 <- design2 %>% mutate(names = ID) %>%
arrange(Day, Elk, Rep, names) %>%
mutate(ID = seq_along(ID)) %>%
mutate(ID=factor(ID, levels=ID))
rownames(design2) <- design2$names
design <- design2
n <- nrow(design)
n## [1] 60pander("table Elk")table Elk
table(design$Elk)##
## 1 2 3 4
## 15 15 15 15pander("table Elk * Rep")table Elk * Rep
table(design$Elk, design$Rep)##
## 1 2 3
## 1 5 5 5
## 2 5 5 5
## 3 5 5 5
## 4 5 5 5pander("table Day * Elk")table Day * Elk
table(design$Day, design$Elk)##
## 1 2 3 4
## 0 3 3 3 3
## 1 3 3 3 3
## 3 3 3 3 3
## 7 3 3 3 3
## 14 3 3 3 3starting point can be a number of datasets
# pdf(file.path(fig_path, "HSD_outcomes.pdf"), width = 8, height = 5,
# pointsize = 16)
outcomes_step1 <- df4.CLRspp
# outcomes_step1 <- df2.CLRasv
# outcomes_step1 <- df3.CLRgen
# outcomes_step1 <- df3.CLRgen_no141.1 Data dimensions and frequencies
pander("dim(design)")dim(design)
pander(paste(dim(design),collapse = " x "))60 x 6
pander("dim(outcomes)")dim(outcomes)
pander(paste(dim(outcomes_step1),collapse = " x "))60 x 162
pander("table(design$Tube, design$Sampling, design$Time)")table(design\(Tube, design\)Sampling, design$Time)
pander(table(design$Rep, design$Elk, design$Day))| 0 | 1 | 3 | 7 | 14 | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 2 | 1 | 1 | 1 | 1 | 1 | ||
| 3 | 1 | 1 | 1 | 1 | 1 | ||
| 4 | 1 | 1 | 1 | 1 | 1 | ||
| 2 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 2 | 1 | 1 | 1 | 1 | 1 | ||
| 3 | 1 | 1 | 1 | 1 | 1 | ||
| 4 | 1 | 1 | 1 | 1 | 1 | ||
| 3 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 2 | 1 | 1 | 1 | 1 | 1 | ||
| 3 | 1 | 1 | 1 | 1 | 1 | ||
| 4 | 1 | 1 | 1 | 1 | 1 |
spectmat <- outcomes_step1
Elk <- design$Elk
Rep <- design$Rep
Day <- design$Day1.2 Hotelling T^2
model = mdatools::pca(spectmat, scale = FALSE,
info = 'Simple PCA model', lim.type = "jm")
ncomp <- 3
Qlim <- model$Qlim
T2lim <- model$T2lim
rownames(Qlim)[2] <- rownames(T2lim)[2] <- "Out_limit"
plot(c(1:5),c(1:5))
# In case of PCA the critical limits are just shown
# on residual plot as lines and can be used for detection
# of extreme objects (solid line) and outliers (dashed line).
plot_hotelling <- function(){
xlim <- range(model$calres$T2[,ncomp])
xlim[1] <- xlim[1]*0.9
xlim[2] <- xlim[2]*1.1
ylim <- range(model$calres$Q[,ncomp])
ylim[1] <- ylim[1]*0.9
ylim[2] <- ylim[2]*2
plot(model$calres$T2[,ncomp], model$calres$Q[,ncomp],
main = "Diagnostic plot for score and residual outliers", xlab = "Hotelling T2 distance",
ylab ="Squared residual distance", pch = 16, xlim = xlim, ylim = ylim)
abline(h=Qlim["Out_limit",ncomp], v=T2lim["Out_limit",ncomp], lty =3)
legend("topright", legend = "Outlier limit", lty = 3)
index1 <- which(model$calres$T2[,ncomp]>=T2lim["Out_limit",ncomp])
index2 <- which(model$calres$Q[,ncomp]>=Qlim["Out_limit",ncomp])
index_ho <- unique(c(index1,index2))
# text(x = model$calres$T2[index_ho,ncomp], y=model$calres$Q[index_ho,ncomp],
# labels = names(model$calres$T2[index_ho,ncomp]), pos = c(1,2,3,4))
}
# pdf(file.path(fig_path,"HSD_hotelling_CLR_spp.pdf"), height = 6, width = 6,
# pointsize = 12)
plot_hotelling()
# dev.off()2 Distribution of the raw outcome variables
2.1 spectmat
pander("spectmat")
par(mfrow=c(1,2))
for (i in 1:ncol(spectmat)){
d = density(spectmat[,i])
plot(d)
}3 Dimension reduction by PCA
Scree plot
###################################################
# Dimension reduction by PCA
###################################################
# ===== PCA ===== #
res_pca <- SVDforPCA(x = spectmat)
### screePlot
df <- data.frame(PC =as.character(1:length(res_pca$var)),
var = res_pca$var)
df <- df[c(1:9),]
screePlot <- ggplot(df, aes(y=0,yend=var,x=PC,
xend=PC))+ geom_segment()+
labs(title= "Scree \nplot",
x = "PC", y="% var")+theme_classic()
screePlot
pander("var explained per PC")var explained per PC
pander(round(res_pca$var[1:8],2))| PC1 | PC2 | PC3 | PC4 | PC5 | PC6 | PC7 | PC8 |
|---|---|---|---|---|---|---|---|
| 14.26 | 12.09 | 9.39 | 7.82 | 4.08 | 3.37 | 3.16 | 2.73 |
Score plots
### score plot
score1 <- DrawScores(res_pca, axes=c(1,2),drawNames = FALSE,
main = "PCA scores plot",
pch = Day,
color= Elk, size = 3) #+
# coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score1.2 <- DrawScores(res_pca, axes=c(3,4),drawNames = FALSE,
main = "PCA scores plot",
pch = Day,
color= Elk, size = 3)#+
# coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
col <- gg_color_hue(2)
score2 <- DrawScores(res_pca, axes=c(1,2),drawNames = FALSE,
main = "Scores plot",
color = Elk,
size = 3)#+
# coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
# pdf(file.path(fig_path,"ScoresSpectmat.pdf"), height = 3.2, width = 9.4)
plot_grid(score1,score2, align = "none", nrow = 1)
# dev.off()
# score1
# score2Score plot grid
score_rep1 <- DrawScores(res_pca, color = design$Rep, main="Aitchison dist. PC1 & PC2", size = 3, axes=c(1,2), drawNames = F)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score_rep2 <- DrawScores(res_pca, color = design$Rep, main="PC3 & PC4", size = 3, axes=c(3,4), drawNames = F)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score_elk1 <- DrawScores(res_pca, color = design$Elk, size = 3, axes=c(1,2), drawNames = FALSE)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score_elk2 <- DrawScores(res_pca, color = design$Elk, size = 3, axes=c(3,4), drawNames = FALSE)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score_Day1 <- DrawScores(res_pca, color = design$Day, size = 3, axes=c(1,2), drawNames = FALSE)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
score_Day2 <- DrawScores(res_pca, color = design$Day, size = 3, axes=c(3,4), drawNames = FALSE)+
coord_cartesian(xlim = c(-20, 20), ylim = c(-20, 20), expand = c(0,0))
# pdf(file.path(fig_path,"ScoresSpectmatPC1-4.pdf"), height = 12, width = 10)
plot_grid(score_rep1, score_rep2, score_elk1, score_elk2, score_Day1, score_Day2,
align = "none", nrow = 3)
# dev.off()3.0.1 Graphs
## Article journal graph
loadPlot <- DrawLoadings(res_pca, type.obj = "PCA",
main = "Loadings plots",
axes = c(1, 2), loadingstype = "s",
ang = "90", ylab = c(""),xaxis_size = 8,
xaxis_type="character",nxaxis = 20,
xlab = "ASV")[[1]]
loadPlot2 <- DrawLoadings(res_pca, type.obj = "PCA",
main = "Loadings plots",
axes = c(1:4), loadingstype = "s",
ang = "90", ylab = c(""),xaxis_size = 8,
xaxis_type="character",nxaxis = 20,
xlab = "ASV")[[1]]
PCA_plots <- ggarrange(screePlot, score1, loadPlot,
ncol = 3, nrow = 1,
widths = c(0.3, 1, 0.85))
# PCA_plots
# ggsave(PCA_plots,
# filename = file.path(fig_path,paste0(Vers,
# "HSD_PCA_outcomes_CLR_spp.pdf")),
# height = 6, width = 14, scale=0.65)
score_plots_comb <- ggarrange(score1 + theme(legend.position="none"),
score1.2+ theme(legend.position="none"),
ncol = 1, nrow = 2, common.legend = F,
legend = NULL)
# Extract the legend. Returns a gtable
leg <- get_legend(score1)
# Convert to a ggplot and print
leg <- as_ggplot(leg)
leg <- leg+ theme(plot.margin = unit(c(30,30,30,30), "points"))
p1 <- ggplot() + theme_void()
scree_plots_comb <- ggarrange(leg, screePlot,
ncol = 1, nrow = 2, common.legend = F)
PCA_plots2 <- ggarrange(scree_plots_comb, score_plots_comb, loadPlot2,
ncol = 3, nrow = 1,
widths = c(0.35, 1, 0.85),
heights = c(0.5,1,0.95))
PCA_plots2
# ggsave(PCA_plots2,
# filename = file.path(fig_path,paste0(Vers,
# "HSD_PCA_outcomesPC1to4.pdf")),
# height = 10, width = 14, scale=0.65)
score2 <- score2+
theme(legend.key.height = unit(0.5, "cm"))
p <- ggarrange(screePlot, loadPlot,
ncol = 2, nrow = 1,
widths = c(0.3,0.95))
PCA_plots3 <- ggarrange(p, score1,
ncol = 1, nrow = 2)
# PCA_plots3
# ggsave(file.path(fig_path,paste0(Vers,"HSD_PCA_outcomes_vertical.pdf")),
# plot = PCA_plots,
# height = 10, width = 6.5, scale=0.75)
# score1 <- score1+
# theme(legend.key.height = unit(0.5, "cm"))
# score1.2 <- score1.2+
# theme(legend.key.height = unit(0.5, "cm"))
#
# p <- ggarrange(screePlot, loadPlot2,
# ncol = 2, nrow = 1,
# widths = c(0.3,0.95))
#
# PCA_plots <- ggarrange(p, score1, score1.2,
# ncol = 1, nrow = 3, heights = c(1,1.3,1.3),
# common.legend = T, legend = "bottom")
#
# PCA_plots3.1 Apply first step of LiMMPCA (PCA)
3.1.1 transform outcomes??
# transform outcomes??
transfo = FALSE
if (transfo){
outcomes <- log(outcomes + 0.01)
}# apply first step of LiMMPCA with dimreducPCA()
res_pca2 <- dimreducPCA(data = as.matrix(outcomes_step1), pcvar = 95)
spectra_PCA_scores <- res_pca2$pca_scores
spectra_PCA_loadings <- res_pca2$pca_loadings
m <- nPC <- dim(spectra_PCA_scores)[2]
pander("Number of PCs kept:")Number of PCs kept:
m## [1] 40# balanced ??
balanced=FALSE
if (balanced){
spectra_PCA_scores_bal <- spectra_PCA_scores[rownames(spectra_PCA_scores) %in%
rownames(design_balanced), ]
design <- design_balanced
spectra_PCA_scores <- spectra_PCA_scores_bal
}4 Parallel mixed modelling
###################################################
# Parallel mixed modelling
###################################################
### define the input arguments for the parallel mixed modelling
# formula
# form <- "~ Time + Tube + (1|Volunteer) + (1|Volunteer:Sampling) "
# form <- "~ Day + (1|Rep) + (1|Elk)" #ideal
form <- "~ Day * Elk + (1|Rep)"
# form <- "~ Day * Elk + (1|Rep) + (1|Elk) + (1|Rep:Elk)"
# form <- "~ Day + (1|Elk) + (1|Elk:Day) + (1|Rep) + (1|Elk:Rep) + (1|Day:Rep)" #ideal
# form <- "~ Day + (1|Elk/Rep)" # NO NEED for this, it explains the same variation as above
# form <- "~ Time + (1|Elk) + (1|Rep) " #cont variables do not work
# multivariate response matrix
outcomes_step2 <- spectra_PCA_scores
# REML
REML <- TRUE
### run parlmer: lmer in parrallel on each response vector
res.parlmer <- parlmer(design, outcomes_step2, form, REML)
MM_full <- res.parlmer
# save the results
RanModMatlist <- res.parlmer$RanModMatlist
FixedModMatlist <- res.parlmer$FixedModMatlist
# Residuals sd error
Res_std_error_PC <- sapply(MM_full$merMod_obj, sigma)
# Residuals
Residuals_PC <- sapply(MM_full$merMod_obj, residuals)
### ranef_PC: Extract the modes of the random effects
ranef_PC <- sapply(MM_full$merMod_obj, function(x) unlist(ranef(x)))
# recover accurate rownames and colnames of ranef_PC
list_rownam <- lapply(ranef(MM_full$merMod_obj[[1]]), rownames)
colnam <- paste0(names(ranef(MM_full$merMod_obj[[1]])), lapply(ranef(MM_full$merMod_obj[[1]]), rownames))
ranef_PC <- sapply(MM_full$merMod_obj, function(x) unlist(ranef(x)))
names(list_rownam) <- gsub("[^A-z]", "", names(list_rownam))
colnam <- c()
for (i in 1:length(list_rownam)){
colnam <- c(colnam, paste0(names(list_rownam)[i], list_rownam[[i]]))
}
rownames(ranef_PC) <- colnam
rownames(ranef_PC) <- gsub("..(Intercept))", "", rownames(ranef_PC))
### fixef: Extract fixed-effects estimates
fixef_PC <- sapply(MM_full$merMod_obj, fixef)
### all fixed estimates and random predictions
cof_PC <- rbind(fixef_PC, ranef_PC)
### Extract Variance and Correlation Components
varcor_random_full <- sapply(MM_full$merMod_obj, VarCorr) # var
dat <- as.numeric(rbind(varcor_random_full))
varcor_random_full_mat <- matrix(dat, nrow=length(varcor_random_full)[1],
dimnames = list(names(varcor_random_full)))
fixNames <- MM_full$fixNames # names of fixed effects
ranNames <- MM_full$ranNames # names of random effects
# estimated Std.Dev. of fixed effects parameters
varcor_fixed_full <- sapply(MM_full$merMod_obj,
function(x) sqrt(diag(vcov(x)))) # Std.Dev.
rownames(varcor_fixed_full) <- rownames(vcov(MM_full$merMod_obj[[1]]))5 Normality of the model residuals
# pdf(file.path(out_path, "HSD_residuals.pdf"), height = 15, width = 10)
par(mfrow=c(8,4), mar=c(2,2,2,2))
ncol(Residuals_PC) #51## [1] 40for (i in 1:15){
qqPlot(Residuals_PC[,i], main = paste0("qqplot - PC",i),
ylab="Residuals quantiles")
d = density(Residuals_PC[,i])
hist(Residuals_PC[,i], main = paste0("Histogram - PC",i), xlab="",
breaks = 20)
}
# dev.off()
6 Effect matrix computation
###################################################
# Effect matrix computation
###################################################
# fixed effects + intercept -----------------------------
dim1FixedModMad <- sapply(FixedModMatlist, function(x) dim(x)[2])
names_FixedEffects <- names(FixedModMatlist)
shortFixedNames <- names_FixedEffects
Xmat <- do.call(cbind, FixedModMatlist)
# colnames(Xmat) %in% rownames(fixef_PC)
Xmat <- Xmat[,rownames(fixef_PC)] # reorder colnames of Xmat
index <- cumsum(dim1FixedModMad)
k <- 1
Mfix <- vector("list", length=length(shortFixedNames))
Mfix_PC <- vector("list", length=length(shortFixedNames))
names(Mfix) <- names(Mfix_PC) <- shortFixedNames
for (i in 1:length(shortFixedNames)){
XMfix = Xmat
XMfix[,-c(k:index[i])] = 0
Mfix_PC[[i]] = XMfix %*% fixef_PC
Mfix[[i]] <- Mfix_PC[[i]]%*%t(spectra_PCA_loadings)
k <- index[i] + 1
dimnames(Mfix[[i]]) <- dimnames(spectmat)
rownames(Mfix_PC[[i]]) <- rownames(spectmat)
}
M0 <- Mfix$Intercept
Mfix <- Mfix[-which(names(Mfix)=="(Intercept)")]
Mfix_PC <- Mfix_PC[-which(names(Mfix_PC)=="(Intercept)")]
# random effects -----------------------------
dim1RandModMad <- sapply(RanModMatlist, function(x) dim(x)[2])
names_randomEffects <- names(RanModMatlist)
shortRandNames <- gsub("[^A-z]", "", names_randomEffects)
Zmat <- do.call(cbind, RanModMatlist)
colnames(Zmat) <- paste0(rep(shortRandNames,
dim1RandModMad),
colnames(Zmat))
# colnames(Zmat) %in% rownames(ranef_PC)
Zmat <- Zmat[,rownames(ranef_PC)] # reorder colnames of Zmat
index <- cumsum(dim1RandModMad)
k <- 1
Mrand_PC <- vector("list", length=length(ranNames))
Mrand <- vector("list", length=length(ranNames))
names(Mrand) <- names(Mrand_PC) <- ranNames
for (i in 1:length(shortRandNames)){
XMrand = Zmat
XMrand[,-c(k:index[i])] = 0
Mrand_PC[[i]] = XMrand %*% ranef_PC
Mrand[[i]] <- Mrand_PC[[i]]%*%t(spectra_PCA_loadings)
k <- index[i] + 1
dimnames(Mrand[[i]]) <- dimnames(spectmat)
rownames(Mrand_PC[[i]]) <- rownames(spectmat)
}
Mres_PC <- Residuals_PC
Mres <- Mres_PC%*%t(spectra_PCA_loadings)7 PCA on the effect matrices
7.1 PCA on the pure effect matrices
7.1.1 Scree plots and pure loadings
Note that only the loadings are backtransformed
# ======================================
# Scree plots and pure loadings ========
# ======================================
# Time
#####################
res_pca <- SVDforPCA(Mfix_PC$Day)
df <- data.frame(PC = as.character(1:7),var = res_pca$var[1:7])
screeplotTime <- ggplot(df, aes(y=0,yend=var,x=PC,
xend=PC))+ geom_segment()+
labs(title= "Scree plot",
x = "PC", y="% var")+theme_classic()
pander("screeplot Time") screeplot Time
screeplotTime
backtransf_load <- t(t(res_pca$loadings) %*% t(spectra_PCA_loadings))
colnames(backtransf_load) <- paste0("L",
1:ncol(backtransf_load),
" (",round(res_pca$var,2),"%)")
loadTime <- LinePlot(t(backtransf_load), rows=c(1:4),
nxaxis = 20,ang = "90", xaxis_type = "character",
main = "PCA loadings",
xlab = "asv", type = "s")[[1]]
pander("loadings Time") loadings Time
loadTime
# Elk
#####################
res_pca <- SVDforPCA(Mfix_PC$Elk)
df <- data.frame(PC = as.character(1:7),var = res_pca$var[1:7])
screeplotElk <- ggplot(df, aes(y=0,yend=var,x=PC,
xend=PC))+ geom_segment()+
labs(title= "Scree plot",
x = "PC", y="% var")+theme_classic()
pander("screeplot Elk") screeplot Elk
screeplotElk
backtransf_load <- t(t(res_pca$loadings) %*% t(spectra_PCA_loadings))
colnames(backtransf_load) <- paste0("L",
1:ncol(backtransf_load),
" (",round(res_pca$var,2),"%)")
loadElk <- LinePlot(t(backtransf_load), rows=c(1:3),
nxaxis = 20,ang = "90", xaxis_type = "character",
main = "PCA loadings",
xlab = "asv", type = "s")[[1]]
pander("loadings Elk") loadings Elk
loadElk
# Sampling
#####################
res_pca <- SVDforPCA(Mrand_PC$Rep)
df <- data.frame(PC = as.character(1:7),var = res_pca$var[1:7])
screeplotSampling <- ggplot(df, aes(y=0,yend=var,x=PC,
xend=PC))+ geom_segment()+
labs(title= "Scree plot",
x = "PC", y="% var")+theme_classic()
pander("screeplot Sampling") screeplot Sampling
screeplotSampling
backtransf_load <- t(t(res_pca$loadings) %*% t(spectra_PCA_loadings))
colnames(backtransf_load) <- paste0("L",
1:ncol(backtransf_load),
" (",round(res_pca$var,2),"%)")
loadSampling <- LinePlot(t(backtransf_load), rows=c(1,2),
nxaxis = 20,ang = "90", xaxis_type = "character",
main = "PCA loadings",
xlab = "asv", type = "s")[[1]]
pander("loadings Sampling")loadings Sampling
loadSampling
# # Volunteer
# #####################
# res_pca <- SVDforPCA(Mrand_PC$Elk)
#
# df <- data.frame(PC = as.character(1:7),var = res_pca$var[1:7])
# screeplotVolunteer <- ggplot(df, aes(y=0,yend=var,x=PC,
# xend=PC))+ geom_segment()+
# labs(title= "Scree plot",
# x = "PC", y="% var")+theme_classic()
# pander("screeplot Volunteer")
# screeplotVolunteer
#
# backtransf_load <- t(t(res_pca$loadings) %*% t(spectra_PCA_loadings))
# colnames(backtransf_load) <- paste0("L",
# 1:ncol(backtransf_load),
# " (",round(res_pca$var,2),"%)")
#
# backtransf_load[,2] <- backtransf_load[,2] *-1
#
# loadVolunteer <- LinePlot(t(backtransf_load), rows=c(1,2,3),
# nxaxis = 20,ang = "90", xaxis_type = "character",
# main = "PCA loadings",
# xlab = "asv", type = "s")[[1]]
# pander("loadings Volunteer")
# loadVolunteer7.2 PCA on the augmented effect matrices
7.2.1 addSegments function
addSegments <- function(group, data, pch=16, main = NULL,
col = rainbow(n = length(unique(group))),
...) {
group <- as.factor(group)
plot(data$x, data$y, col=col[group], pch=pch, main=main, ...)
group <- as.factor(group)
xcent <- tapply(data[,1], group, FUN=mean)
ycent <- tapply(data[,2], group, FUN=mean)
centers <- data.frame(xcent=xcent, ycent=ycent)
mapply(FUN = points, x = centers$xcent,
y = centers$ycent, col = col,
MoreArgs = list(pch=20, cex=0.7))
submatrices <- split(x=data, f=group)
for (i in 1:nlevels(group)){
mapply(FUN = segments, x1 = submatrices[[i]]$x,
y1 = submatrices[[i]]$y, col = col[i],
MoreArgs = list(x0 = centers$xcent[i],
y0 = centers$ycent[i]))
}
}7.2.2 Augmented (with ANOVA degrees of freedom) scores plots (ASCA-E)
# ========================
# augmented scores =======
# ========================
# * Tube: Mu + E
# * Time: Mt + E
# * Volunteer: Mv + Ms
# * Sampling: Ms + E
# correction factors ++++++
# a <- nlevels(design$Tube)
# b <- nlevels(design$Time)
# c <- nlevels(design$Volunteer)
# d <- nlevels(design$Sampling)
b <- nlevels(design$Day)
c <- nlevels(design$Elk)
d <- nlevels(design$Rep)
#################################
### Augmented time effect
#################################
pander("Augmented Time effect")Augmented Time effect
res_pca <- SVDforPCA(Mfix_PC$Day)
df1 <- (b-1)
df2 <- (b*c*d-b-c*d+2)
Fstat <- qf(.95, df1=df1, df2=df2)
coef <- sqrt(Fstat*df1/df2)
res_pca$scores[,1:2] <- (Mfix_PC$Day + Mres_PC*coef)%*%res_pca$loadings[,1:2]
col <- c("1"=violetred, "2" = darkblue)
pch <- c("1"= 2, "2"= 4)
# index <- c(84, 85, 87, 88)
# PC1lab <- paste0("PC", 1, " (", round(res_pca$var[1], 2),"%)")
df <- as.data.frame(res_pca$scores)
Time_scores <- ggplot(aes(y=PC1, x= Day, color=Day,
shape = Elk),data=df)+
geom_jitter() +
ggtitle(label = "PCA Scores")+
xlab("Day")+ #ylim(low=-2.1, high=2.1) +
geom_hline(yintercept=0, linetype=2, color="gray", size=0.7)+
theme(plot.title = element_text(face="plain"),axis.text.x = element_text(size=10)) +
theme_bw()
# annotate("text", y = res_pca$scores[index,1]+ 0.1*c(1,1,1,1),
# x = index, label = rownames(res_pca$scores)[index])
Time_scores
#################################
### Augmented Elk effect
#################################
pander("Augmented Elk effect")Augmented Elk effect
res_pca <- SVDforPCA(Mfix_PC$Elk)
df1 <- (c-1)
df2 <- (b*c*d-b-c*d+2)
Fstat <- qf(.95, df1=df1, df2=df2)
coef <- sqrt(Fstat*df1/df2)
res_pca$scores[,1:2] <- (Mfix_PC$Elk + Mres_PC*coef)%*%res_pca$loadings[,1:2]
col <- c("1"=violetred, "2" = darkblue)
pch <- c("1"= 2, "2"= 4)
# index <- c(84, 85, 87, 88)
# PC1lab <- paste0("PC", 1, " (", round(res_pca$var[1], 2),"%)")
df <- as.data.frame(res_pca$scores)
Elk_scores <- ggplot(aes(y=PC1, x= Day, color=Elk, group = Elk,
shape = Day),data=df)+
geom_jitter() +
# geom_point()+
labs(title = "PCA Scores",
x = "Day", y = "PC1") +
geom_hline(yintercept=0, linetype=2, color="gray", size=0.7)+
theme(plot.title = element_text(face="plain"),axis.text.x = element_text(size=10))+
theme_bw()
# annotate("text", y = res_pca$scores[index,1]+ 0.1*c(1,1,1,1),
# x = index, label = rownames(res_pca$scores)[index])
Elk_scores
#plot 2
xlab <- paste0("PC", 1, " (", round(res_pca$var[1], 2),"%)")
ylab <- paste0("PC", 2, " (", round(res_pca$var[2], 2), "%)")
pch <- c("1"= 1, "2"= 17, "3"=8)
col <- c(darkblue, "dodgerblue", turquoise, violetred,
limegreen,"orangered", "forestgreen", "gold",
"goldenrod4", "orange1", "maroon1",
"red3")
VolSamp <- as.factor(paste0("elk_",Elk,".day_", Day))
Vol <- as.factor(substr(VolSamp,1,5))
# pch <- c("1"= 2, "2"= 8)
names(col) <- levels(Elk)
Elk_scores2 <- ggplot(df, aes(PC1, PC2, group = VolSamp,
shape = Day)) +
geom_point(size = 2, aes(colour = Elk)) +
geom_line(aes(colour = Elk)) +
# scale_shape_manual(name = "Day", values=c(8, 0,17, 1, 2),
# guide=guide_legend(order=1, shape = 1)) +
# coord_cartesian(xlim = c(-5, 5), ylim = c(-10, 10)) +
ggplot2::labs(title = "PCA Scores",
x = xlab, y = ylab) +
ggplot2::geom_vline(xintercept = 0, size = 0.1) +
ggplot2::geom_hline(yintercept = 0, size = 0.1) +
ggplot2::theme_bw() +
ggplot2::theme(panel.grid.major =
ggplot2::element_line(color = "gray60",
size = 0.2),
panel.grid.minor = ggplot2::element_blank(),
panel.background =
ggplot2::element_rect(fill = "gray98")) + theme(legend.text=element_text(size=7),
legend.key.height=unit(0.55,"line"))
# Elk_scores2# #################################
# ### Augmented Volunteer effect
# #################################
#
# pander("Augmented Volunteer effect")
#
# res_pca <- SVDforPCA(Mrand_PC$Elk)
# df1 <- (c-1)
# df2 <- (c*d-c)
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# res_pca$scores[,1:2] <- (Mrand_PC$Elk+
# Mres_PC*coef)%*%
# res_pca$loadings[,1:2]
# res_pca$scores[,2] <- res_pca$scores[,2]*-1
#
# res_pca$scores <- round(res_pca$scores, 6)
# Volunteer_scores <- DrawScores(res_pca,
# main = "PCA Scores",
# color = Elk, pch=Day,
# drawNames = FALSE, drawPolygon = TRUE,
# noLegend = FALSE, size=2)+
# coord_cartesian(xlim = c(-25, 25),
# ylim = c(-25, 25))+
# theme(legend.text=element_text(size=10),
# plot.title = element_text(face="plain"),
# legend.key.height=unit(0.55,"line"))
#
# Volunteer_scores
# #################################
# ### Augmented Day effect
# #################################
#
# pander("Augmented Volunteer effect")
#
# res_pca <- SVDforPCA(Mrand_PC$Day)
# df1 <- (b-1)
# df2 <- (b*c*d-b-c*d+2)
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# res_pca$scores[,1:2] <- (Mrand_PC$Day+
# Mres_PC*coef)%*%
# res_pca$loadings[,1:2]
# res_pca$scores[,2] <- res_pca$scores[,2]*-1
#
# res_pca$scores <- round(res_pca$scores, 6)
# Volunteer_scores <- DrawScores(res_pca,
# main = "PCA Scores",
# color = Elk, pch=Day,
# drawNames = FALSE, drawPolygon = TRUE,
# noLegend = FALSE, size=2)+
# coord_cartesian(xlim = c(-25, 25),
# ylim = c(-25, 25))+
# theme(legend.text=element_text(size=10),
# plot.title = element_text(face="plain"),
# legend.key.height=unit(0.55,"line"))
#
# Volunteer_scores
#################################
### Augmented Sampling effect
#################################
pander("Augmented Sampling effect")Augmented Sampling effect
res_pca <- SVDforPCA(Mrand_PC$Rep)
df1 <- (d-1)
df2 <- (b*c*d-b-c*d+2)
Fstat <- qf(.95, df1=df1, df2=df2)
coef <- sqrt(Fstat*df1/df2)
res_pca$scores[,1:2] <- (Mrand_PC$Rep + Mres_PC*coef)%*%res_pca$loadings[,1:2]
res_pca$scores <- round(res_pca$scores, 6)
Sampling_scores <- DrawScores(res_pca,
main = "PCA Scores",
color = Rep, pch=Elk,
drawNames = FALSE, drawPolygon = TRUE,
noLegend = FALSE, size=2)+
coord_cartesian(xlim = c(-25, 25),
ylim = c(-25, 25))+
theme(legend.text=element_text(size=10),
plot.title = element_text(face="plain"),
legend.key.height=unit(0.55,"line"))
pch <- c("1"= 1, "2"= 17, "3"=8)
col <- c(darkblue, "dodgerblue", turquoise, violetred,
limegreen,"orangered", "forestgreen", "gold",
"goldenrod4", "orange1", "maroon1",
"red3")
VolSamp <- as.factor(paste0("elk_",Elk,".rep_", Rep))
Vol <- as.factor(substr(VolSamp,1,5))
pch <- c("1"= 2, "2"= 8)
names(col) <- levels(Elk)
xlab <- paste0("PC", 1, " (", round(res_pca$var[1], 2),"%)")
ylab <- paste0("PC", 2, " (", round(res_pca$var[2], 2), "%)")
df <- as.data.frame(res_pca$scores[,1:2])
Sampling_scores <- ggplot(df, aes(PC1, PC2, group = VolSamp,
shape = Rep)) +
geom_point(size = 2, aes(colour = Elk)) +
geom_line(aes(colour = Elk)) +
scale_shape_manual(name = "Sampling", values=c(8, 0,17),
guide=guide_legend(order=1, shape = 1)) +
coord_cartesian(xlim = c(-5, 5), ylim = c(-10, 10)) +
ggplot2::labs(title = "PCA Scores",
x = xlab, y = ylab) +
ggplot2::geom_vline(xintercept = 0, size = 0.1) +
ggplot2::geom_hline(yintercept = 0, size = 0.1) +
ggplot2::theme_bw() +
ggplot2::theme(panel.grid.major =
ggplot2::element_line(color = "gray60",
size = 0.2),
panel.grid.minor = ggplot2::element_blank(),
panel.background =
ggplot2::element_rect(fill = "gray98")) + theme(legend.text=element_text(size=7),
legend.key.height=unit(0.55,"line")) + theme_bw()
Sampling_scores
7.2.3 Augmented (with Effective Dimensions) scores plots (ASCA-E)
# Effective Dimensions
# source("ED/metabo_Mixed.R")EDu <- rep((nlevels(design$Rep)-1),ncol(outcomes_step2))
EDt <- rep((nlevels(design$Day)-1),ncol(outcomes_step2))
# EDs <- ED_metabo["ED_Samp",]
# EDv <- ED_metabo["ED_Vol",]
# EDe <- n - colSums(ED_metabo)
EDe <- 20
# ========================
# augmented scores =======
# ========================
# * Tube: Mu + E
# * Time: Mt + E
# * Volunteer: Mv + Ms
# * Sampling: Ms + E
#################################
### Augmented time effect
#################################
# pander("Augmented Time effect")
# res_pca <- SVDforPCA(Mfix_PC$Day)
# df1 <- EDt
# df2 <- EDe
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# mat <- matrix(NA, ncol=ncol(outcomes_step2), nrow=nrow(outcomes_step2))
# for (i in 1:ncol(outcomes_step2)){
# mat[,i] <- Mres_PC[,i]*coef[i]
# }
#
# res_pca$scores[,1:2] <- (Mfix_PC$Day + mat)%*%res_pca$loadings[,1:2]
#
# col <- c("1"=violetred, "2" = darkblue)
# pch <- c("1"= 2, "2"= 4)
# # index <- c(84, 85, 87, 88)
#
# df <- as.data.frame(res_pca$scores)
#
# Time_scores <- ggplot(aes(y=PC1, x= 1:nrow(df), color=Day,
# shape = Rep),data=df)+
# geom_point() +
# ggtitle(label = "PCA Scores")+
# xlab("Observation number")+ #ylim(low=-2.1, high=2.1) +
# geom_hline(yintercept=0, linetype=2, color="gray", size=0.7)+
# theme(plot.title = element_text(face="plain"),axis.text.x = element_text(size=10)) #+
# # annotate("text", y = res_pca$scores[index,1]+ 0.1*c(1,1,1,1),
# # x = index, label = rownames(res_pca$scores)[index])
# Time_scores
#################################
### Augmented tube effect
#################################
# pander("Augmented Tube effect")
# res_pca <- SVDforPCA(Mfix_PC$Elk)
# df1 <- EDu
# df2 <- EDe
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# mat <- matrix(NA, ncol=ncol(outcomes_step2), nrow=nrow(outcomes_step2))
# for (i in 1:ncol(outcomes_step2)){
# mat[,i] <- Mres_PC[,i]*coef[i]
# }
#
# res_pca$scores[,1:2] <- (Mfix_PC$Elk + mat)%*%res_pca$loadings[,1:2]
#
# col <- c("1"=violetred, "2" = darkblue)
# pch <- c("1"= 2, "2"= 4)
#
# # index <- c(80,79, 84,81,78,22,19,18,21,87)
# df <- as.data.frame(res_pca$scores)
#
# Tube_scores <- ggplot(aes(y=PC1, x= 1:nrow(df),
# color=Elk, shape = Day),
# data=df) +
# geom_point() +
# ggtitle(label = "PCA Scores")+
# xlab("Observation number")+
# geom_hline(yintercept=0, linetype=2, color="gray", size=0.7)+
# theme(plot.title = element_text(face="plain"),
# axis.text.x = element_text(size=10)) #+
# # annotate("text",
# # y = res_pca$scores[index,1]+ 0.2*
# # c(1,1,-1,1,-1,1, -1,-1,1,-1),
# # x = index, label = rownames(res_pca$scores)[index])
#
# Tube_scores
#################################
### Augmented Volunteer effect
#################################
# pander("Augmented Volunteer effect")
#
# res_pca <- SVDforPCA(Mrand_PC$Volunteer)
# df1 <- EDv
# df2 <- EDs
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# mat <- matrix(NA, ncol=ncol(outcomes), nrow=nrow(outcomes))
# for (i in 1:ncol(Mrand_PC$Sampling)){
# mat[,i] <- Mrand_PC$Sampling[,i]*coef[i]
# }
#
# res_pca$scores[,1:2] <- (Mrand_PC$Volunteer+mat)%*%
# res_pca$loadings[,1:2]
# res_pca$scores[,2] <- res_pca$scores[,2]*-1
#
# res_pca$scores <- round(res_pca$scores, 6)
# Volunteer_scores <- DrawScores(res_pca,
# main = "PCA Scores",
# color = Volunteer, pch=Volunteer,
# drawNames = FALSE, drawPolygon = TRUE,
# noLegend = FALSE, size=2)+
# coord_cartesian(xlim = c(-50, 50),
# ylim = c(-17, 17))+
# theme(legend.text=element_text(size=10),
# plot.title = element_text(face="plain"),
# legend.key.height=unit(0.55,"line"))
#
# Volunteer_scores
#################################
### Augmented Sampling effect
#################################
# pander("Augmented Sampling effect")
#
# res_pca <- SVDforPCA(Mrand_PC$Sampling)
# df1 <- EDs
# df2 <- EDe
# Fstat <- qf(.95, df1=df1, df2=df2)
# coef <- sqrt(Fstat*df1/df2)
#
# mat <- matrix(NA, ncol=ncol(outcomes), nrow=nrow(outcomes))
# for (i in 1:ncol(outcomes)){
# mat[,i] <- Mres_PC[,i]*coef[i]
# }
#
# res_pca$scores[,1:2] <- (Mrand_PC$Sampling + mat)%*%res_pca$loadings[,1:2]
#
# res_pca$scores <- round(res_pca$scores, 6)
#
# pch <- c("1"= 1, "2"= 17, "3"=8)
#
# col <- c(darkblue, "dodgerblue", turquoise, violetred,
# limegreen,"orangered", "forestgreen", "gold",
# "goldenrod4", "orange1", "maroon1",
# "red3")
#
# VolSamp <- as.factor(paste0(Volunteer, Sampling))
# Vol <- as.factor(substr(VolSamp,1,2))
# pch <- c("1"= 2, "2"= 8)
# names(col) <- levels(Volunteer)
#
# xlab <- paste0("PC", 1, " (", round(res_pca$var[1], 2),"%)")
# ylab <- paste0("PC", 2, " (", round(res_pca$var[2], 2), "%)")
#
# df <- as.data.frame(res_pca$scores[,1:2])
# Sampling_scores <- ggplot(df, aes(PC1, PC2, group = VolSamp,
# shape = Sampling)) +
# geom_point(size = 2, aes(colour = Volunteer)) +
# geom_line(aes(colour = Volunteer)) +
# scale_shape_manual(name = "Sampling", values=c(8, 0,17),
# guide=guide_legend(order=1, shape = 1)) +
# coord_cartesian(xlim = c(-26, 26), ylim = c(-12, 12)) +
# ggplot2::labs(title = "PCA Scores",
# x = xlab, y = ylab) +
# ggplot2::geom_vline(xintercept = 0, size = 0.1) +
# ggplot2::geom_hline(yintercept = 0, size = 0.1) +
# ggplot2::theme_bw() +
# ggplot2::theme(panel.grid.major =
# ggplot2::element_line(color = "gray60",
# size = 0.2),
# panel.grid.minor = ggplot2::element_blank(),
# panel.background =
# ggplot2::element_rect(fill = "gray98")) + theme(legend.text=element_text(size=10),
# legend.key.height=unit(0.55,"line"))
#
#
# Sampling_scoresPlots
### Thesis chapter output
Time_scores <- Time_scores + theme(text=element_text(size=12))
loadTime <- loadTime + theme(text=element_text(size=12))
a <- grid.arrange(screeplotTime, Time_scores,
loadTime, nrow=1,widths=c(0.3, 1, 1),
top=textGrob("Time effect matrix",
gp=gpar(fontsize=20,font=2)))
Elk_scores <- Elk_scores + theme(text=element_text(size=12))
loadElk <- loadElk + theme(text=element_text(size=12))
b <- grid.arrange(screeplotElk,
Elk_scores,loadElk,
nrow=1,widths=c(0.3, 1, 1),
top=textGrob("Elk effect matrix",
gp=gpar(fontsize=20,font=2)))
Sampling_scores <- Sampling_scores + theme(text=element_text(size=12))
loadSampling <- loadSampling + theme(text=element_text(size=12))
c <- grid.arrange(screeplotSampling,
Sampling_scores,loadSampling,
nrow=1,widths=c(0.3, 1, 1),
top=textGrob("Sampling effect matrix",
gp=gpar(fontsize=20,font=2)))
## Thesis chapter output
# pdf(file.path(fig_path,paste0(Vers,
# "HSD_Scores_Loadings_EffectMat_backtrans.pdf")),
# height = 20, width = 14)
ggarrange(a,b,c, nrow=3, labels = c("A", "B", "C"))
# dev.off()
# plots <- ggarrange(a,b, nrow=2, labels = c("A", "B"))
# plots
# ggsave(file.path(fig_path,paste0(Vers,
# "HSD_Scores_Loadings_EffectMat_backtrans1.pdf")), plots,
# height = 10, width = 15, scale=0.68)
# plots <- ggarrange(c,d, nrow=2, labels = c("C", "D"))
# plots
# ggsave(file.path(fig_path,paste0(Vers,
# "HSD_Scores_Loadings_EffectMat_backtrans2.pdf")), plots,
# height = 10, width = 15, scale=0.68)7.2.4 Residuals
res_pca <- SVDforPCA(Mres_PC)
df <- data.frame(PC = as.character(1:length(res_pca$var)),
var = res_pca$var)
df <- df[1:7,]
screeplot_resid <- ggplot(df, aes(y=0,yend=var,x=PC,
xend=PC))+ geom_segment() +
labs(title= "Scree plot",
x = "PC", y="% var") + theme_classic()
backtransf_load <- t(t(res_pca$loadings) %*% t(spectra_PCA_loadings))
colnames(backtransf_load) <- paste0("L",
1:ncol(backtransf_load),
" (",round(res_pca$var,2),"%)")
loadings_resid <- LinePlot(t(backtransf_load), rows=c(1,2),
main = "PCA loadings",
xaxis_type = "character",ang = "90", nxaxis = 20,
xlab = "asv", type = "s")[[1]]
loadings_resid <- loadings_resid + theme(text=element_text(size=12))
# index <- c(85, 84, 80, 81, 79, 78)
res_pca <- SVDforPCA(Mres_PC)
scores_resid <- DrawScores(res_pca, drawNames = FALSE,
# xaxis_type = "character",ang = "90", nxaxis = 20,
color = Day,
pch = Elk, main ="PCA scores",
size = 2) +
# annotate("text", y = (res_pca$scores[index,2]+0.3 +
# 0.4*c( 1 , 1, 1, 1,-1,1)),
# x = res_pca$scores[index,1]+0.3,
# label = rownames(res_pca$scores[index,1:2]))+
theme(legend.text=element_text(size=10),
text=element_text(size=12),
legend.key.height=unit(0.7,"line"))
# scores_resid <- scores_resid + coord_cartesian(xlim = c(-9, 9),
# ylim = c(-9, 9))
# scores_resid
plots <- grid.arrange(screeplot_resid,
scores_resid, loadings_resid,
nrow=1,widths = c(0.3, 1, 1),
top=textGrob("Residual effect matrix",
gp=gpar(fontsize=20,font=2)))
# plots
# ggsave(filename = paste0(fig_path,"/HSD_Scores_Loadings_Residuals.pdf"),
# plot = plots, device = "pdf", height = 6, width = 12, scale = 0.9)plots combined
### Journal article output
e <- grid.arrange(screeplot_resid,
scores_resid, loadings_resid,
nrow=1,widths = c(0.3, 1, 1),
top=textGrob("Residual effect matrix",
gp=gpar(fontsize=20,font=2)))
# journal article output
# pdf(file.path(fig_path,paste0(Vers,
# "HSD_Scores_Loadings_EffectMat.pdf")),
# height = 22, width = 14)
p <- ggarrange(a,b,c,e , nrow=4, labels = c("A", "B", "C", "D"))
p
# dev.off()
# ggsave(file.path(fig_path,paste0(Vers,
# "HSD_Scores_Loadings_EffectMat.pdf")), plot = p,
# height = 22, width = 14, scale = 0.8)8 Percentage of explained variance
8.1 Method from Nakagawa and Schielzeth (2012)
####################################################
# Pourcentage de variance expliquée
####################################################
# Random effects -----------------------------------
sigma2_res = Res_std_error_PC^2 # Residual
varcor_random_full <- as.data.frame(varcor_random_full)
Var_Mrand <- rbind(varcor_random_full,
sigma2_res=sigma2_res)
Var_Mrand <- data.matrix(Var_Mrand)
ranNames <- rownames(varcor_random_full)
# fixed effects -----------------------------------
# Mfix_PC[1]
Var_Mfix <- c()
for (i in 1:length(fixNames)){
# variance of parameter values (population)
Var_Mfix <- rbind(Var_Mfix,
(apply(Mfix_PC[[i]], 2, var) *(n - 1) / n))
}
rownames(Var_Mfix) <- fixNames
rownames(Var_Mrand) <- c(ranNames, "Residuals")
Var_Mrand <- rbind(
# Elk=Var_Mrand["Elk",],
# Day=Var_Mrand["Day",],
# Elk_Day=Var_Mrand["Elk:Day",],
# Day_Rep=Var_Mrand["Day:Rep",],
# Elk_Rep=Var_Mrand["Elk:Rep",],
# Rep=Var_Mrand["Rep",],
Residuals=Var_Mrand["Residuals",])
# All variance components (fixed and random) +++++
var_comp <- rbind(Var_Mfix, Var_Mrand)
# log of variance components +++++
log_var_comp <- t(log1p(var_comp)) # log(x+1)
log_var_comp <- cbind(id=1:dim(log_var_comp)[1],
log_var_comp)
log_var_comp <- as.data.frame(log_var_comp)
log_var_comp$id <- str_pad(1:dim(log_var_comp)[1], 2, pad = "0")
log_var_comp <- reshape2::melt(log_var_comp, id=c("id"))
log_var_comp$value <- as.numeric(log_var_comp$value)
names(log_var_comp) <- c("PC", "Effect", "Variance")
sum_var_comp <- rowSums(var_comp)
# Percent variance explained by each effect -----
var_comp_m1_abs <- sum_var_comp
var_comp_m1 <- var_comp_m1_abs*100/sum(var_comp_m1_abs)
names(var_comp_m1) <- names(var_comp_m1_abs)
# pdf(file.path(fig_path,"variance_components.pdf"),
# height = 3, width = 3, pointsize = 12)
xlim <- c(0, ceiling(max(var_comp_m1)/10) * 10)
par(mar=c(0.5,2,3,0.5))
barplot(var_comp_m1,
main="Variance components \n percentage",
xaxt="n",las=2, col=c(darkblue, turquoise,violetred ,
limegreen, gray67), border = NA,
legend = names(var_comp_m1),
args.legend = list(x="topleft", inset=c(0,0),
box.lty=0,cex = 1,
y.intersp = 0.8))
# dev.off()
table_var <- rbind(var_comp_m1_abs, var_comp_m1)
rownames(table_var) <- c("Sum variance for all responses",
"percentage of variation")
colnames(table_var) <- rownames(var_comp)
pander(table_var)| Â | Day | Elk | Day:Elk | Residuals |
|---|---|---|---|---|
| Sum variance for all responses | 75.09 | 175.7 | 113.9 | 438.2 |
| percentage of variation | 9.351 | 21.88 | 14.19 | 54.58 |
## Chapter graph
gg_color_hue <- function(n) {
hues = seq(15, 375, length = n + 1)
hcl(h = hues, l = 65, c = 100)[1:n]
}
p <- ggplot(log_var_comp, aes(Effect, Variance, group = PC))+
ggtitle("HSD - Log of variance components")+
scale_color_manual(values = setNames(gg_color_hue(nPC),
levels(log_var_comp$PC)))
p <- p + geom_point(aes(colour = PC))+
geom_line(aes(colour = PC,linetype=PC),size=0.5)+
ylim(c(0,5)) +
ylab(label = "log(variance)") +
theme(legend.text=element_text(size=10),
legend.key.height=unit(0.7,"line"))+
scale_linetype_manual(values = 1:nPC)+
theme_classic()+
theme(legend.key.width = unit(0.8,"cm"),
plot.title = element_text(size = 17),
axis.title.y = element_text(size = 17),
axis.title.x = element_text(size = 17),
axis.text = element_text(size = 13),
legend.text = element_text(size = 12),
legend.title = element_text(size = 17),
legend.key.height = unit(0.5, "cm"))
# names(var_comp_m1)[5] <- "Residuals"
# p
# Thesis chapter output
# ggexport(p, filename = file.path(fig_path,
# paste0(Vers,"HSD_variance_components.pdf")),
# height = 5, width = 6.5, pointsize=20)## Article journal graph
tab <- data.frame(Effect= names(var_comp_m1),
pcvar = round(var_comp_m1,2))
var_comp_m1.table <- ggpubr::ggtexttable(tab,
cols = c("Effect", "Global var (%)"),
rows = NULL, theme = ggpubr::ttheme("classic",
base_size = 10))
p <- p + annotation_custom(ggplotGrob(var_comp_m1.table),
xmin = 2.3, ymin = 3.8,
xmax = 0)
p
# ggexport(p, filename = file.path(fig_path,paste0(Vers,"ETS_variance_components_table.pdf")),
# height = 6, width = 9, pointsize=16)8.2 Method from Rousseau, 2011
fix_var <- (1/2)*2*(fixef_PC[2,]^2) # Method from Rousseau, 2011 for the fixed effects
var_comp <- rbind(fix_var, Var_Mrand)
sum_var_comp <- apply(var_comp, 1, sum)
pander( "sum of the variance components over the responses")sum of the variance components over the responses
pander(sum_var_comp)| fix_var | Residuals |
|---|---|
| 111.4 | 438.2 |
sum_var_comp <- sum_var_comp*100/sum(sum_var_comp)
names(sum_var_comp) <- rownames(var_comp)
barplot(sum_var_comp)
pander(sum_var_comp)| fix_var | Residuals |
|---|---|
| 20.27 | 79.73 |
9 Bootstrap
# set up of the bootstrap
set.seed(2017)
nsim = 2000 # number of simulations
# name of the output
name <- paste0("bootstrap_ELKtimeSeries_VSTT_repRandom.RData")
# Set up -------------------
# formulas without the effect to test
null_formulas <- list(
Volunteer = "~ Day + (1|Rep) ",
Sampling = "~ Day + (1|Elk) ",
# Tube = "~ Day + (1|Volunteer) + (1|Volunteer:Sampling)",
Time = "~ Day + (1|Elk) + (1|Elk:Rep)")
null_effects <- names(null_formulas)
REML <- c(TRUE, TRUE, FALSE) # REML option for each null formula
names(REML) <- names(null_formulas)# coding for the Volunteer:Sampling interaction
VS <- paste0("elk", design$Elk, ".", design$Rep)
design$VS <- VS9.1 Likelihood Ratio computation
##################################################
# True log-likelihood Ratio statistics #
##################################################
# full model: MM_full
######################
# REML ++++++
loglik_PC_full_REML <- sapply(MM_full$merMod_obj, logLik, REML=T)
mean_loglik_PC_full_REML <- mean(loglik_PC_full_REML)
# ML (REML==FALSE) ++++++
loglik_PC_full_ML <- sapply(MM_full$merMod_obj, logLik, REML=F)
mean_loglik_PC_full_ML <- mean(loglik_PC_full_ML)
loglik_PC_full <- matrix(NA, ncol = nPC,
nrow=length(null_formulas), byrow = TRUE)
for (i in 1:length(REML)){
if (REML[i]==TRUE){
loglik_PC_full[i,] <- loglik_PC_full_REML
}else {loglik_PC_full[i,] <- loglik_PC_full_ML}
}
mean_loglik_PC_full <- rep(mean_loglik_PC_full_ML,
length(null_formulas))
mean_loglik_PC_full[REML] <- mean_loglik_PC_full_REML
# Null models
######################
res.parlmer_NULL <- vector("list", length = length(null_formulas))
names(res.parlmer_NULL) <- names(REML) <- names(null_formulas)
for (i in 1:length(null_formulas)) {
# run parlmer
res.parlmer_NULL[[i]] <- parlmer(design,
outcomes_step2, null_formulas[[i]], REML=REML[i])
}
# Save the results ------------
MM_PC_null <- lapply(res.parlmer_NULL, function(x) x[["merMod_obj"]])
ranNames <- sapply(res.parlmer_NULL, function(x) x[["ranNames"]])
Fixvarnames <- lapply(res.parlmer_NULL, function(x) x[["fixNames"]])
varcor_random <- vector(mode = "list", length = length(null_formulas))
fixef_PC <- vector(mode = "list", length = length(null_formulas))
modmat_fixed <- vector(mode = "list", length = length(null_formulas))
M0 <- vector(mode = "list", length = length(null_formulas))
for (i in 1:length(null_formulas)){
varcor_random[[i]] <- sapply(MM_PC_null[[i]],
function(x)
as.data.frame(VarCorr(x))$vcov)
rownames(varcor_random[[i]]) <- c(names(VarCorr(MM_PC_null[[i]][[1]])),
"Residual")
fixef_PC[[i]] <- sapply(MM_PC_null[[i]], fixef)
modmat_fixed[[i]] <- model.matrix(MM_PC_null[[i]][[1]], type = "fixed")
# intercept
XM0 <- modmat_fixed[[i]]
XM0[,-1] <- 0
M0_PC <- XM0%*%fixef_PC[[i]]
M0[[i]] <- M0_PC%*%t(spectra_PCA_loadings)
}
# Effect matrices computation ------------
index <- vector("list", length=length(null_formulas))
fixNames_int <- lapply(Fixvarnames, function(x) c("(Intercept)", x))
colnam <- lapply(modmat_fixed, colnames)
index <- vector("list", length=length(Fixvarnames))
for (i in 1:length(null_formulas)){
id <- c()
for (k in 1:length(fixNames_int[[i]])){
id <- c(id, grep(fixNames_int[[i]][[k]], colnam[[i]]))
}
index[[i]] <- id
}
Mfix <- Mfix_PC <- vector("list", length=length(null_formulas))
names(Mfix) <- names(fixNames_int)
for (i in 1:length(null_formulas)){
XMfix = modmat_fixed[[i]]
XMfix[,-c(index[[i]])] = 0
Mfix_PC[[i]] = XMfix %*% fixef_PC[[i]] # Matrix of the Group effect
# backtransform the PC to original coefficients
Mfix[[i]] <- Mfix_PC[[i]]%*%t(spectra_PCA_loadings)
}
fitted_values_PC <- Mfix
######################
# compute the LRT
######################
# objects initialisation ------------
Res_std_error_PC_null <- vector("list", length=length(null_formulas))
loglik_PC_null <- vector("list", length=length(null_formulas))
mean_loglik_PC_null <- c()
meanlog <- c()
sumlog <- c()
### compute the LRT ----------------------------
for (i in 1:length(null_formulas)){
Res_std_error_PC_null[[i]] <- sapply(MM_PC_null[[i]], sigma)
# meanlog and sumlog
loglik_PC_null[[i]] <- sapply(MM_PC_null[[i]], logLik, REML=REML[i])
mean_loglik_PC_null[i] <- mean(loglik_PC_null[[i]])
meanlog[i] <- -2*(mean_loglik_PC_null[i] /mean_loglik_PC_full[i])
sumlog[i] <- 2*(sum(loglik_PC_full[i,] - loglik_PC_null[[i]]))
}
names(meanlog) <- names(null_formulas)
names(sumlog) <- names(null_formulas)
# Graphs ----------------------------
col1="blue"
col2="red"
par(mar=c(4,3,2,6))
dif <- vector(mode = "list")
for (i in 1:length(null_formulas)){
# graphs
mat <- cbind(loglik_PC_null[[i]], loglik_PC_full[i,])
rownames(mat) <- paste0("PC", 1:nPC)
col <- c(col1,col2)
par(xpd=TRUE)
barplot(t(mat), beside=T, ylab="Log-likelihood",
cex.names=0.8, las=2, col=col,
main = paste("log-likelihoods",names(null_formulas)[i]),
xpd=TRUE)
legend("topright", legend = c("loglik restricted","loglik full"),
fill = col, bty = "n", inset=c(-0.1,0))
dif[[i]] <- 2*(mat[,2] - mat[,1]) # log-likelihood difference
}
difmat <- do.call(cbind, dif)
colnames(difmat) <- names(null_formulas)
col=c(darkblue,turquoise,violetred)
barplot(t(difmat), beside = TRUE, col=col,
main = "Log-likelihood ratios")
legend("topright", legend = names(null_formulas),
title = "Removed effect", col = col, pch=15)
9.2 Booststrap tests
### Bootstrap ---------------------------------------
# bootstrapLT input arguments:
# MM_null = MM_PC_null$Sampling
# useREML=TRUE
# null_formula <- null_formulas[[2]]
bootstrapLT <- function(null_effect, useREML, MM_null, null_formula) {
# simulate y from the null models --------
nPC <- length(MM_null)
simulatedY <- c()
for (i in 1:nPC){
ysim <- unlist(simulate(MM_null[[i]], re.form=NA))
simulatedY <- cbind(simulatedY, ysim)
}
y <- simulatedY
dimnames(y) <- dimnames(outcomes_step2)
# build restricted model -------
# print("null")
f_null <- parlmer(design, outcomes = y, null_formula, REML=useREML)
# build full model -------
# print("full")
f_full <- parlmer(design, outcomes = y, form, REML=useREML)
MM_f_null <- f_null$merMod_obj
MM_f_full <- f_full$merMod_obj
# LR -------
loglikelihood_null <- sapply(MM_f_null, logLik, REML=useREML)
mean_loglikelihood_null <- mean(loglikelihood_null)
loglikelihood_full <- sapply(MM_f_full, logLik, REML=useREML)
mean_loglikelihood_full <- mean(loglikelihood_full)
sumlog <- 2*(sum(loglikelihood_full - loglikelihood_null))
sumlog
}
sumlog_boot <- vector("list", length=length(null_formulas))
system.time(
for (i in 1:length(null_formulas)){
null_effect <- null_effects[i]
print(null_effect)
sumlog_boot[[i]] = replicate(nsim,
bootstrapLT(null_effect = null_effect,
MM_null = MM_PC_null[[null_effect]],
useREML =REML[null_effect],
null_formula = null_formulas[[null_effect]]),
simplify = TRUE)
}
)
save(sumlog_boot, sumlog, file = file.path(data_path, name))load(file=file.path(data_path, name))9.3 Drawings
9.3.1 Histogram drawings
names(sumlog_boot) <- casefold(names(null_formulas), upper = FALSE)
# plot.new
######################
# Time
######################
# pdf(file = file.path(fig_path, "ETS_hist_Time.pdf"),
# width = 7, height = 5, pointsize = 15)
par(mar=c(2.1, 2.1, 3, 2), xpd=TRUE, mfrow=c(1,1))
df <- nPC * 1 # df for Time and Tube
m=hist(sumlog_boot$time, freq=F, breaks=100,
xlab="Global Likelihood Ratio Statistic",
xlim=range(sumlog["Time"], sumlog_boot$time),
ylim = c(0,0.02),
col = "gray75",border = "gray75",
main = " Fixed Time effect", cex.main = 2.2)
lines(density(sumlog_boot$time), col=darkblue,lwd=2, lty=2)
lines(dchisq(seq(0,max(sumlog_boot$time)), df), col= "chartreuse4", lwd = 2)
points(sumlog["Time"], 0, col="red", pch=19, lwd=6)
legend("topright",
legend = c(paste0("True GLRT: ", round(sumlog["Time"],2)),
"Kernel density", paste0("chi2 distrib. (df=", df,")")),
col = c("red", darkblue, "chartreuse4"),
lty=c(NA,2,1),pch=c(19,NA,NA),
inset=c(0,0),box.lty=0, cex = 1.4, y.intersp = 0.8, lwd=c(4))
# dev.off()
######################
# Volunteer
######################
# pdf(file = file.path(fig_path, "ETS_hist_Elk.pdf"),
# width = 7, height = 5, pointsize = 15)
par(mar=c(2.1, 2.1, 3, 2), xpd=TRUE, mfrow=c(1,1))
df <- nPC
m=hist(sumlog_boot$volunteer, freq=F, breaks=100,
xlab="Global Likelihood Ratio Statistic",
xlim=range(sumlog["Volunteer"], sumlog_boot$volunteer),
col = "gray75",border = "gray75",
main = " Fixed Elk effect",
cex.main = 2.2)
lines(density(sumlog_boot$volunteer), col=darkblue,lwd=2, lty=2)
# lines(dchisq(seq(0,max(sumlog_boot$volunteer)), df), col= "chartreuse4", lwd = 2)
points(sumlog["Volunteer"], 0, col="red", pch=19, lwd=6)
legend("topright",
legend = c(paste0("True GLRT: ", round(sumlog["Volunteer"],2)),
"Kernel density"),
col = c("red", darkblue), lty=c(NA,2),pch=c(19,NA),
inset=c(-0,0),box.lty=0, cex = 1.4, y.intersp = 0.8, lwd=c(4))
# dev.off()
######################
# Sampling
######################
# pdf(file = file.path(fig_path, "ETS_hist_Sampling.pdf"),
# width = 7, height = 5, pointsize = 15)
par(mar=c(2.1, 2.1, 3, 2), xpd=TRUE, mfrow=c(1,1))
df <- nPC
m=hist(sumlog_boot$sampling, freq=F, breaks=100,
xlab="Global Likelihood Ratio Statistic",
xlim=range(sumlog["Sampling"], sumlog_boot$sampling),
col = "gray75",border = "gray75",
main = " Random Sampling effect",
cex.main = 2.2)
lines(density(sumlog_boot$sampling), col=darkblue,lwd=2, lty=2)
points(sumlog["Sampling"], 0, col="red", pch=19, lwd=6)
legend("topright",
legend = c(paste0("True GLRT: ", round(sumlog["Sampling"],2)),
"Kernel density"),
col = c("red", darkblue), lty=c(NA,2),pch=c(19,NA),
inset=c(0,0),box.lty=0, cex = 1.4, y.intersp = 0.8, lwd=c(4))
# dev.off()9.3.2 bootstrap p-values
pval <- c()
for (i in 1:length(null_formulas)){
pval[i] <- (sum(sumlog[i]<sumlog_boot[[i]])+1)/(nsim+1)
}
names(pval) <- names(null_formulas)
pander("p-values")p-values
pander(pval)| Volunteer | Sampling | Time |
|---|---|---|
| 0.0004998 | 0.1624 | 0.1959 |
9.4 p-value based on chi2 distribution for fixed effects
pander("true GLLR:")true GLLR:
sumlog["Time"]## Time
## 845.4103df <- 1*nPC
curve(dchisq(x, df=df), col='red', main = "Chi-Square Density Graph",
from=0,to=60)
pander("p-value Time")p-value Time
pchisq(sumlog["Time"], df=df, lower.tail=FALSE)## Time
## 1.782515e-151pander("p-value Elk")p-value Elk
pchisq(sumlog["Volunteer"], df=df, lower.tail=FALSE)## Volunteer
## 09.4.1 Graph
difmat <- do.call(cbind, dif)
difmat <- data.frame(PC=substr(rownames(difmat),3,4), difmat)
colnames(difmat) <- c("PC", names(null_formulas))
difmat <- gather(difmat, key=Effect, value = value, Time, Volunteer, Sampling)
difmat$Effect <- factor(difmat$Effect, levels = c("Time", "Volunteer", "Sampling"))
difmat$PC <- factor(difmat$PC, levels = as.character(c(1:40)))
class(difmat$PC)## [1] "factor"# difmat$Effect
LLRplot <- ggplot(data=difmat, aes(x=PC, y=value, fill = Effect)) +
geom_bar(width=0.8,stat="identity", position=position_dodge(width=0.8)) +
theme_classic()+labs(title="(Restricted) Log-likelihood Ratios") +
ylab(label="(R)LLR") +
guides(fill=guide_legend(title="Removed effect"))
LLRplot
tab <- round(pval, 4)
tab[1:3] <- paste("<", round(pval, 4))
tab <- data.frame(Effect = names(tab), `p-value` = tab) #,
# chi2 = c("<5e-04","<5e-04","-", "-"))
pval_boot.table <- ggtexttable(tab,cols = c("Effect",
"Boostrapped p-value"),
# "Chi2 test"),
rows = NULL,
theme=ttheme(base_size = 9))
LLR_pval_plot <- LLRplot + annotation_custom(ggplotGrob(pval_boot.table),
xmin=33, xmax=33,
ymin=125, ymax=150) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
# LLR_pval_plot <- ggarrange(LLRplot, pval_boot.table,
# ncol = 1, nrow = 2,
# heights = c(1, 0.3), common.legend=TRUE)
# ggexport(LLR_pval_plot, filename = file.path(fig_path,"ETS_LLR_pval_plot.pdf"),
# height = 6, width = 5)
LLR_pval_plot
# journal article output
ggsave(LLR_pval_plot, filename = file.path(fig_path,paste0(Vers,"ETS_GLLR.pdf")),
width=10, height=6, scale=0.85)### Chapter graph
difmat <- do.call(cbind, dif)
difmat <- data.frame(PC=substr(rownames(difmat),3,4), difmat)
colnames(difmat) <- c("PC", names(null_formulas))
difmat <- gather(difmat, key=Effect, value = value, Volunteer, Sampling, Time)
difmat$Effect <- as.factor(difmat$Effect)
difmat$Effect <- factor(difmat$Effect,levels(difmat$Effect)[c(4,1,3,2)])
difmat2 <- cbind(Time=difmat[difmat$Effect=="Time", "value"],
# Tube=difmat[difmat$Effect=="Tube", "value"],
Volunteer=difmat[difmat$Effect=="Volunteer", "value"],
Sampling=difmat[difmat$Effect=="Sampling", "value"]
)
rownames(difmat2) <- c(1:dim(difmat2)[1])
gg_color_hue <- function(n) {
hues = seq(15, 375, length = n + 1)
hcl(h = hues, l = 65, c = 100)[1:n]
}
# pdf(file.path(fig_path, paste0(Vers,"ETS_GLLR.pdf")),width=13,
# height=8, pointsize = 20)
par(mar=c(4,4,4,1), cex=1.2)
# plotting settings -------------------------------------------------------
ylim <- range(mat)*c(1,1.5)
angle1 <- rep(c(45,45,135), length.out=4)
angle2 <- rep(c(45,135,135), length.out=4)
density1 <- seq(5,35,length.out=4)
density2 <- seq(5,35,length.out=4)
angle1 <- rev(angle1)
angle2 <- rev(angle2)
density1 <- rev(density1)
density2 <- rev(density2)
barplot(t(difmat2), beside=TRUE,col = gg_color_hue(4),ylab="(R)LLR",
xlab="PC", ylim=range(pretty(c(0,difmat2))),
main = "(Restricted) Log-likelihood Ratios",
angle=angle1, density=density1)
barplot(t(difmat2), beside=TRUE, add=TRUE, col = gg_color_hue(4),
ylab="(R)LLR", xlab="PC",
main = "(Restricted) Log-likelihood Ratios",
angle=angle2, density=density2)
legend("topright", legend = colnames(difmat2),
title = "Removed effect:", col = gg_color_hue(4),
fill=gg_color_hue(4),angle=angle1, density=density1,
xpd=TRUE, inset=c(0,-0.1), bty="n")
par(bg="transparent")
legend("topright", legend = colnames(difmat2),
title = "Removed effect:", col = gg_color_hue(4),
fill=gg_color_hue(4),angle=angle2, density=density2, bty="n",
xpd=TRUE, inset=c(0,-0.1))
# dev.off()
# pdf(file.path(fig_path, paste0(Vers,"ETS_pval.pdf")))
pval_boot.table
# dev.off()10 Session info
sessionInfo()## R version 4.1.2 (2021-11-01)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: CentOS Linux 7 (Core)
##
## Matrix products: default
## BLAS/LAPACK: /usr/lib64/libopenblasp-r0.3.3.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] grid stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] phyloseq_1.38.0 RColorBrewer_1.1-2 car_3.0-12 carData_3.0-5
## [5] mdatools_0.12.0 tidyr_1.2.0 ggpubr_0.4.0 stringr_1.4.0
## [9] gridExtra_2.3 reshape2_1.4.4 cowplot_1.1.1 ggplot2_3.3.5
## [13] pander_0.6.5 dplyr_1.0.8 plyr_1.8.6 lme4_1.1-28
## [17] Matrix_1.4-0 MBXUCL_0.1 ezknitr_0.6
##
## loaded via a namespace (and not attached):
## [1] backports_1.4.1 igraph_1.2.11 splines_4.1.2
## [4] listenv_0.8.0 GenomeInfoDb_1.30.1 digest_0.6.29
## [7] foreach_1.5.2 htmltools_0.5.2 fansi_1.0.2
## [10] magrittr_2.0.2 cluster_2.1.2 recipes_0.1.17
## [13] globals_0.14.0 Biostrings_2.62.0 gower_1.0.0
## [16] bdsmatrix_1.3-4 prettyunits_1.1.1 colorspace_2.0-3
## [19] xfun_0.29 crayon_1.5.0 RCurl_1.98-1.6
## [22] jsonlite_1.8.0 survival_3.2-13 iterators_1.0.14
## [25] ape_5.6-1 glue_1.6.2 gtable_0.3.0
## [28] ipred_0.9-12 zlibbioc_1.40.0 XVector_0.34.0
## [31] genalg_0.2.0 spls_2.2-3 Rhdf5lib_1.16.0
## [34] future.apply_1.8.1 BiocGenerics_0.40.0 abind_1.4-5
## [37] scales_1.1.1 mvtnorm_1.1-3 DBI_1.1.2
## [40] plsVarSel_0.9.7 rstatix_0.7.0 Rcpp_1.0.8
## [43] progress_1.2.2 ropls_1.26.4 proxy_0.4-26
## [46] stats4_4.1.2 lava_1.6.10 prodlim_2019.11.13
## [49] htmlwidgets_1.5.4 ellipsis_0.3.2 farver_2.1.0
## [52] pkgconfig_2.0.3 nnet_7.3-16 sass_0.4.0
## [55] utf8_1.2.2 caret_6.0-90 labeling_0.4.2
## [58] tidyselect_1.1.2 rlang_1.0.1 munsell_0.5.0
## [61] phyclust_0.1-30 tools_4.1.2 cli_3.2.0
## [64] generics_0.1.2 ade4_1.7-18 pls_2.8-0
## [67] broom_0.7.12 evaluate_0.15 biomformat_1.22.0
## [70] fastmap_1.1.0 yaml_2.3.5 ModelMetrics_1.2.2.2
## [73] knitr_1.37 rgl_0.108.3 purrr_0.3.4
## [76] future_1.23.0 nlme_3.1-153 praznik_10.0.0
## [79] compiler_4.1.2 rstudioapi_0.13 MSQC_1.0.2
## [82] ggsignif_0.6.3 tibble_3.1.6 bslib_0.3.1
## [85] stringi_1.7.6 highr_0.9 lattice_0.20-45
## [88] nloptr_2.0.0 vegan_2.5-7 permute_0.9-7
## [91] multtest_2.50.0 vctrs_0.3.8 pillar_1.7.0
## [94] lifecycle_1.0.1 rhdf5filters_1.6.0 jquerylib_0.1.4
## [97] data.table_1.14.2 bitops_1.0-7 R6_2.5.1
## [100] IRanges_2.28.0 parallelly_1.30.0 codetools_0.2-18
## [103] boot_1.3-28 MASS_7.3-54 assertthat_0.2.1
## [106] rhdf5_2.38.0 rprojroot_2.0.2 withr_2.4.3
## [109] S4Vectors_0.32.3 GenomeInfoDbData_1.2.7 mgcv_1.8-38
## [112] parallel_4.1.2 hms_1.1.1 rpart_4.1-15
## [115] timeDate_3043.102 class_7.3-19 minqa_1.2.4
## [118] clValid_0.7 rmarkdown_2.11 pROC_1.18.0
## [121] Biobase_2.54.0 lubridate_1.8.0